The Stringy Quantum Hall Fluid

TL;DR

This paper establishes a string theory framework connecting non-commutative Chern-Simons theory with the fractional quantum Hall fluid, modeling electrons as D-particles and explaining fractional charges and statistics.

Contribution

It introduces a novel string-theoretic model for the fractional quantum Hall effect using branes and non-commutative geometry, providing explicit correspondences and physical interpretations.

Findings

D-particles model electrons in the quantum Hall fluid

Fractional charges and statistics are realized as string endpoints

The filling fraction relates to D-brane ratios

Abstract

Using branes in massive Type IIA string theory, and a novel decoupling limit, we provide an explicit correspondence between non-commutative Chern-Simons theory and the fractional quantum Hall fluid. The role of the electrons is played by D-particles, the background magnetic field corresponds to a RR 2-form flux, and the two-dimensional fluid is described by non-commutative D2-branes. The filling fraction is given by the ratio of the number of D2-branes and the number of D8-branes, and therefore by the ratio rank/level of the Chern-Simons gauge theory. Quasiparticles and quasiholes are realized as endpoints of fundamental strings on the D2-branes, and are found to possess fractional D-particle charges and fractional statistics.